Functional Two-sample Tests Based on Empirical Characteristic Functionals

Two-sample tests for functional data based on empirical characteristic functionals are proposed. The test statistic is of Cramer–von Mises type with integration over a preselected family of probability measures, say Q, leading a computationaly feasible and powerful test statistic. The choice of the probability measure Q is discussed and the empirical size and power of the resulting two-sample functional tests are investigated in a small simulation study.